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Would it be possible to make something like two metal balls, one positively charged and one negatively charged, in space, where the negatively charged ball would orbit the positively charged one like a moon orbiting a planet or like a macroscopic Rutherford model atom?

Would it be possible to make on earth by making the charge strong enough to counteract gravity?

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As safkan & Brionius have said, as a first guess the resulting orbit is just as stable as a normal Newtonian one. There is a catch however.

The problem with this planetary system is exactly the same as with the Rutherford atom. As the electron travels around the nucleus it is being accelerated towards the centre. As a result it emits electromagnetic waves. This reduces the energy of the electron so it will move towards the nucleus. In a very short time it will collide with the nucleus.That's why Bohr came up with his, better, model, with the electrons in "shells" obeying quantum rules.

Exactly the same thing will happen with your planet, albeit it on a much slower time scale.

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  • $\begingroup$ Another consideration for metal balls is that the distribution of charge on each ball will no longer be spherical! That would be a very interesting problem to solve because the charge separation distance could be different from the separation of centers of mass. $\endgroup$
    – Bill N
    Jan 28, 2016 at 3:26
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The overall problem with magnetic or electrically charged objects "orbiting" each other is that those forces decay by the square of distance. So if you can get an object into a perfectly circular orbit at exactly the right speed, it works; but if the orbiting "moon" every strays out of that, the unstable orbit collapses quickly and the "moon" falls into the "planet."

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  • $\begingroup$ In classical Newtonian gravitation, the form of the force is exactly the same as the electrical force -- inverse square force. And we do know for a fact that orbits of planets under this force are not "unstable" -- we can even analyze the motion with what we call gravitational perturbation theory. One real problem when charged bodies orbit each other is radiation -- an accelerating charged body will lose energy by electromagnetic radiation, and the orbits will then decay. This was the trouble with Rutherford's model of the atom. $\endgroup$
    – safkan
    Jan 27, 2016 at 22:15
  • $\begingroup$ Yeah, agree with safkan, these orbits would be no more unstable than those in classical Newtonian gravity, which are stable (elliptical and circular alike). $\endgroup$
    – Brionius
    Jan 27, 2016 at 22:33

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